線性代數(英文維基教科書)
The book was designed specifically for students who had not previously been exposed to mathematics as mathematicians view it. That is, as a subject whose goal is to rigorously prove theorems starting from clear consistent definitions. This book attempts to build students up from a background where mathematics is simply a tool that provides useful calculations to the point where the students have a grasp of the clear and precise nature of mathematics. A more detailed discussion of the prerequisites and goal of this book is given in the introduction.
這本書是專門為那些以前沒有接觸過數學的學生設計的,因為他們是數學家。也就是說,作為一個目標是從清晰一致的定義開始嚴格證明定理的學科。這本書試圖建立學生從一個背景,數學只是一個工具,提供有用的計算點,學生有一個清晰和精確的數學性質的掌握。引言中對本書的先決條件和目標進行了更詳細的討論。
這本教科書翻譯自英文維基教科書Linear Algebra,相關的翻譯問題可見討論頁。
Table of Contents 目錄[編輯]
Linear Systems 線性方程組[編輯]
- Solving Linear Systems 求解線性方程組(2020年12月9日)
- Linear Geometry of n-Space
- Reduced Echelon Form
- Topic: Computer Algebra Systems
- Topic: Input-Output Analysis
- Input-Output Analysis M File
- Topic: Accuracy of Computations
- Topic: Analyzing Networks
- Topic: Speed of Gauss' Method
Vector Spaces [編輯]
- Definition of Vector Space
- Linear Independence
- Basis and Dimension
- Topic: Fields
- Topic: Crystals
- Topic: Voting Paradoxes
- Topic: Dimensional Analysis
Maps Between Spaces[編輯]
- Isomorphisms
- Homomorphisms
- Computing Linear Maps
- Matrix Operations
- Change of Basis
- Projection
- Topic: Line of Best Fit
- Topic: Geometry of Linear Maps
- Topic: Markov Chains
- Topic: Orthonormal Matrices
Determinants[編輯]
- Definition
- Geometry of Determinants
- Other Formulas for Determinants
- Topic: Cramer's Rule
- Topic: Speed of Calculating Determinants
- Topic: Projective Geometry
Similarity[編輯]
- Complex Vector Spaces
- Similarity
- Nilpotence
- Jordan Form
- Topic: Geometry of Eigenvalues
- Topic: The Method of Powers
- Topic: Stable Populations
- Topic: Linear Recurrences
Unitary Transformations[編輯]
Appendix[編輯]
Resources and Licensing[編輯]
- Licensing And History
- Resources
- Bibliography (see individual pages for references)
- Index